the weekly wages of 1000 workers are normally distributed around a mean of rs 70 and with a sd of 5.estimate the number of workers whoes weekle wages will be between 70 and 72. also estimate the lowest wages of the 100 highest paid workers
Answers
Answer:
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Answer:
Step-by-step explanation:
Number of workers whose weekly wages between 70 and 72:
z = x-μ/ σ
So, when x = 70, z becomes 0 and when x = 72, z becomes 0.4
ie P(0<z<0.4)
The table value of area under standard deviation(z) of 0.4 is 0.1554
No of workers = 0.1554 × 1000 = 155
The lowest wages of the 100 highest paid workers:
No. of workers: 100 (given)
Total no. of workers: 1000
Probability of 100 workers: 100/1000 = 0.1
Let a be the value of z when probability = 0.1 on the right side
ie P(z>a) = 0.1
Therefore, P(0<z<a) = 0.5-0.1 = 0.40
When z = 1.28, table value is 0.3997 is approximately equal to 0.40
ie P(0<z<1.28) = 0.40
So, a = 1.28 ie the value of z = 1.28
But z = x-μ/ σ
1.28 = x-70/5
Therefore, x = ₹76.4